2013-03-04T06:35:50ZFluxBBhttp://www.mathisfunforum.com/viewtopic.php?id=19056Well, 1/x *sqrt(1+1/x^4) is everywhere greater than 1/x, so its integral on any interval will be greater than the integral of 1/x on the same interval!]]>http://www.mathisfunforum.com/profile.php?id=1187862013-03-04T06:35:50Zhttp://www.mathisfunforum.com/viewtopic.php?pid=256205#p256205Divergence should be proven or shown...I think this solution can be used as a prove, but maybe there is an easier way?

And I repeat the question: Why Wikipedia uses incomplete formula?

]]>http://www.mathisfunforum.com/profile.php?id=580932013-03-04T05:11:13Zhttp://www.mathisfunforum.com/viewtopic.php?pid=256195#p256195It is definitely divergent. The integral does not exist.]]>http://www.mathisfunforum.com/profile.php?id=337902013-03-04T00:19:11Zhttp://www.mathisfunforum.com/viewtopic.php?pid=256101#p256101I would say that that is divergent, then.]]>http://www.mathisfunforum.com/profile.php?id=1187862013-03-04T00:12:23Zhttp://www.mathisfunforum.com/viewtopic.php?pid=256094#p256094Another attempt:Starting from here:

Let Then:

We have a formula #24 in the table of integrals in the textbook:

So:

And here we have first limit is infinity divided by infinity, second limit is infinity and a constant.Therefore we have an infinity in the final answer...Did I make any mistakes?]]>http://www.mathisfunforum.com/profile.php?id=580932013-03-04T00:06:17Zhttp://www.mathisfunforum.com/viewtopic.php?pid=256089#p256089Hi;

I would have tried the simple numerical method type sub of u = 1 / x in the beginning.

]]>http://www.mathisfunforum.com/profile.php?id=337902013-03-03T23:48:00Zhttp://www.mathisfunforum.com/viewtopic.php?pid=256066#p256066Maybe a substitution v=sqrt(u)? ]]>http://www.mathisfunforum.com/profile.php?id=1187862013-03-03T23:44:41Zhttp://www.mathisfunforum.com/viewtopic.php?pid=256062#p256062Now I wonder myself where did I got u^6 Thanks.

Now I am not sure what to do next?]]>http://www.mathisfunforum.com/profile.php?id=580932013-03-03T23:36:25Zhttp://www.mathisfunforum.com/viewtopic.php?pid=256052#p256052Where did you get 4u^6 in the denominator in the step right after the substitution from?]]>http://www.mathisfunforum.com/profile.php?id=1187862013-03-03T22:56:49Zhttp://www.mathisfunforum.com/viewtopic.php?pid=256011#p256011According to the textbook, the surface area of the curve y=1/x for x>=1, rotated around x-axis is infinite.According to my calculations it is finite. I suspect I have a mistake, but I cannot find it. Please help:

Surface area is:

Here we have a=1, b=\infty, and f(x)=1/xSince one of the bounds is infinity, we have an improper integral and have to do it with a limit:

Looking at the description of Gabriel's Horn in Wikipedia, I see that they used for the surface a function:

Why is that? How did they manage to convert into 1?]]>http://www.mathisfunforum.com/profile.php?id=580932013-03-03T19:19:26Zhttp://www.mathisfunforum.com/viewtopic.php?pid=256001#p256001